Details

sample934.0ms

Algorithm

intervals

Results

344.0ms	71×	body	2560	valid
228.0ms	129×	body	1280	valid
182.0ms	28×	body	5120	valid
95.0ms	87×	body	640	valid
24.0ms	31×	body	320	valid
14.0ms	56×	body	80	valid
8.0ms	15×	body	160	valid

simplify478.0ms

Counts: 1 → 1

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.4b	(* (pow t 3.0) (tan k))
21.2b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.7b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`associate-r` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

7.0ms	(pow (/ k t) 2.0)
30.0ms	(* (pow t 3.0) (tan k))
132.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
98.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.5s

Counts

4 → 12

Calls

4 calls:

120.0ms	(pow (/ k t) 2.0)
351.0ms	(* (pow t 3.0) (tan k))
615.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
389.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify2.3s

Counts: 191 → 191

prune715.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.9b	(* (pow k 2.0) (pow t 1.0))
16.7b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

Calls

4 calls:

30.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
18.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
28.0ms	(* (pow k 2.0) (pow t 1.0))
105.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

516.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
111.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
529.0ms	(* (pow k 2.0) (pow t 1.0))
1.0s	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.8s

Counts: 612 → 612

prune928.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
2.4b	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
6.9b	(* (pow k 2.0) (pow t 1.0))
16.7b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

1169×	`add-exp-log`
660×	`prod-exp`
466×	`div-exp`
367×	`pow-exp`
157×	`pow-to-exp`
90×	`times-frac`
88×	`add-sqr-sqrt`
80×	`rec-exp` `1-exp`
61×	`add-cbrt-cube`
55×	`add-cube-cbrt` `*-un-lft-identity`
52×	`associate-r`
31×	`associate-l`
21×	`cbrt-unprod`
20×	`cbrt-undiv`
19×	`unpow-prod-down`
15×	`unswap-sqr`
9×	`sqr-pow`
7×	`pow1` `div-inv`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`-commutative` `associate-/l`
2×	`frac-times` `associate-*l/`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `associate-/r/` `inv-pow`

Counts

4 → 440

Calls

4 calls:

19.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
58.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
27.0ms	(* (pow k 2.0) (pow t 1.0))
131.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series1.9s

Counts

4 → 12

Calls

4 calls:

480.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
86.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
463.0ms	(* (pow k 2.0) (pow t 1.0))
898.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify1.0s

Counts: 452 → 452

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

localize392.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.2b	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l)) (* (fabs (sin k)) (/ (fabs (sin k)) l)))
6.9b	(* (pow k 2.0) (pow t 1.0))
8.8b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

1274×	`add-exp-log`
782×	`prod-exp`
448×	`div-exp`
416×	`pow-exp`
176×	`pow-to-exp`
90×	`rec-exp` `1-exp`
52×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
20×	`cbrt-unprod`
19×	`unpow-prod-down`
18×	`associate-l`
14×	`cbrt-undiv`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unswap-sqr` `sqr-pow`
8×	`associate-r`
7×	`times-frac`
5×	`pow1`
4×	`associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative`
1×	`pow-flip` `associate-*r/` `associate-/r/` `inv-pow`

Counts

4 → 404

Calls

4 calls:

38.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
72.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l)) (* (fabs (sin k)) (/ (fabs (sin k)) l)))
36.0ms	(* (pow k 2.0) (pow t 1.0))
93.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l))

series2.4s

Counts

4 → 12

Calls

4 calls:

520.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
900.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l)) (* (fabs (sin k)) (/ (fabs (sin k)) l)))
474.0ms	(* (pow k 2.0) (pow t 1.0))
519.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l))

simplify2.0s

Counts: 416 → 416

prune724.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

regimes796.0ms

Accuracy

19.2% (3.7b remaining)

Error of 10.3b against oracle of 6.6b and baseline of 11.2b

bsearch2.1s

Steps

Iters	Range		Point
9	-2.756710539291077e-150	-1.7550820911137718e-159	-4.293396349092778e-152
8	-1.0810847511793032e+165	-2.467274161490782e+161	-2.5203319264792143e+161

simplify975.0ms

end0.0ms

sample32.3s

Algorithm

intervals

Results

8.7s	4128×	body	1280	valid
8.2s	2246×	body	2560	valid
6.9s	918×	body	5120	valid
4.5s	2543×	body	640	valid
1.7s	1024×	body	320	valid
714.0ms	2021×	body	80	valid
624.0ms	440×	body	160	valid